Sampling of analog signals is an essential step in digital signal processing. An analog signal is in general a function of time and can be represented by a plurality of digitized samples in time domain. The amplitude of each sample then can be quantized to a finite number of bits. This sample-and-quantization process converts an analog signal into digital format. Next, the digitized data can be processed by one or more digital signal processors and the resultant data may be converted back into analog form if needed.
An analog signal can be accurately represented by a stream of time samples only if the analog signal is band-limited to a maximum frequency and the samples are obtained at or above a Nyquist rate which is twice the maximum frequency. An analog prefilter is usually used to filter an input analog signal to limit the bandwidth. Such sampling generates multiple replicas of the band-limited analog signal in the frequency domain which are separated from one another by a frequency separation equal to the sampling frequency. Thus, the sampling frequency should be sufficiently large to ensure that two adjacent replicas do not overlap. At a given sampling frequency which is equal or greater than the Nyquist rate, the analog prefilter may need to have a sharp frequency fall-off profile which often requires expensive and bulky high-quality analog filters. Therefore, it may be advantageous to oversample the analog signal, i.e., at a sampling frequency higher than the Nyquist rate, in order to alleviate the need for high-quality analog prefilters.
Oversampling may also be used to improve the accuracy or precision of the analog-to-digital conversion by reducing the quantization noise. At a fixed sampling frequency, the accuracy of the analog-to-digital conversion can be increased by reducing the quantization step or increasing the quantization resolution. This reduces the quantization error. However, a high-resolution quantizer can be bulky and expensive. In addition, a high-resolution quantizer may be susceptible to a nonlinear response. Use of a high-resolution quantizer may be avoided by using oversampling in combination with a low-resolution quantizer to maintain a desired accuracy and to improve the circuit linearity. Although the accuracy of each sample is low, the increased number of samples due to the oversampling can be used to improve the overall accuracy. In essence, oversampling allows spreading the quantization noise over a wide frequency range. Since a signal frequency band at low frequencies only occupies a fraction of the wide frequency range, the quantization noise in the signal frequency band can be significantly reduced. The noise remaining in the signal band can be further reduced by a noise shaping technique to shift the frequency of the noise out of the signal band.
For example, analog-to-digital conversion based on the sigma-delta modulation uses a sigma-delta modulator to perform oversampling on an input analog signal at a high sampling rate and noise shaping on the sampled data. In addition, a decimation filter connected to the sigma-delta modulator performs a digital filtering process on the output samples to produce output digital data with an increased data bit length at a desired low sampling rate. This filtering process also attenuates the quantization noise at high frequencies caused by the noise shaping to reduce the noise in the downsampled output digital data.
In general, a decimation filtering circuit may be used in any device to convert an input digital signal of a high sampling rate into an output digital signal of a low sampling rate without losing the information content. The word length of the decimated data can be increased if needed to preserve the resolution. Such a decimation filtering circuit may be used in a number of applications such as modems and digital audio devices.